The difference of the squares of two consecutive numbers is equal to the sum of two numbers: As:
(i) 3 x 3 – 2 x 2 = 3 + 2 = 5
(ii) 9 x 9 – 8 x 8 = 9 + 8 = 17
(iii) 25 x 25 – 24 x 24 = 25 + 24 = 49
(iv) 217 x 217 – 216 x 216 = 217 + 216 = 433
You may write the difference of the squares of two given consecutive numbers:
(i) 76 x 76 – 75 x 75 = _______ .
(ii) 115 x 115 – 114 x 114 = _______ .
(iii) 137 x 137 – 136 x 136 = _______ .
(iv) 376 x 376 – 375 x 375 = _______ .
(v) 695 x 695 - 694 x 694 = _______ .
Check the answers:
(i) 76 x 76 – 75 x 75
= 76 + 75
= 151.
Answer: 151
(ii) 115 x 115 – 114 x 114
= 115 + 114
= 229.
Answer: 229
(iii) 137 x 137 – 136 x 136
= 137 + 136
= 273.
Answer: 273
(iv) 376 x 376 – 375 x 375
= 376 + 375
= 751.
Answer: 751
(v) 695 x 695 - 694 x 694
= 695 + 694
= 1389.
Answer: 1389
Related Concept
● Patterns and Mental Mathematics
● Counting Numbers in Proper Pattern
● Puzzle
● Patterns
4th Grade Math Activities
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